Transitions From Order to Disorder in Multi-Dark and Multi-Dark-Bright Soliton Atomic Clouds

TL;DR

This study investigates how ordered soliton lattices in atomic gases transition to disordered states, using multiple modeling approaches to quantify the gradual loss of order under perturbations.

Contribution

It introduces an empirical order parameter to quantify the transition from order to disorder in soliton gases in one- and two-component atomic systems.

Findings

Order-disorder transition is gradual without a sharp phase change.

The order parameter decreases with increasing perturbations.

Multiple modeling approaches corroborate the transition dynamics.

Abstract

We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas". As our illustrative examples, we use both one-component, as well as two-component, one dimensional atomic gases very close to zero temperature, where in the presence of repulsive inter-atomic interactions and of a parabolic trap, a cloud, respectively of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial differential equation, particle-based ordinary differential equations describing the soliton dynamical system and Monte-Carlo simulations for the particle system. We define an "empirical" order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the "thermally" (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.